Implementation of a dual fabry-perot photonic pressure sensor

ABSTRACT

In an aspect, a pressure sensor for determining pressure in an environment comprises: a source for emitting a coherent reference light characterized by a reference light frequency; a first lock-in mechanism configured to send an electrical signal to the source based on a reference resonance frequency; a reference cavity; wherein the reference cavity is characterized by the reference resonance frequency; a modulator configured a reference light to generate at least a first sideband frequency such that an output of said modulator is a measurement light characterized by at least the first sideband frequency; a frequency synthesizer configured to drive the modulator; a second lock-in mechanism configured to send an electrical signal to the frequency synthesizer based on a measurement resonance frequency; and a measurement cavity configured to receive at least a portion of the measurement light; wherein the measurement cavity is characterized by the measurement resonance frequency; and wherein the pressure of the environment is determined based on the reference resonant frequency and the measurement resonance frequency.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.16/745,671, filed Jan. 17, 2020, which application claims the benefit ofpriority to U.S. Provisional Patent Application Nos. 62/794,179 filedJan. 18, 2019 and 62/880,184 filed Jul. 30, 2019, each of which ishereby incorporated by reference in its entirety.

SUMMARY OF THE INVENTION

Provided herein are pressure sensors and associated methods formeasuring a pressure of an environment. The pressure sensors may bereferred to as photonic pressure sensors. These sensors provide animproved degree of precision within useful ranges of pressure, such as,but not limited to, 1 to 100 kPa. Certain embodiments of these sensorsreduce the number and/or complexity of components compared tocavity-based conventional systems in order to provide for more portableand cost-efficient systems.

In an aspect, a pressure sensor for determining pressure in anenvironment comprises: a source for emitting a coherent reference lightcharacterized by a reference light frequency; a first lock-in mechanismconfigured to send an electrical signal to the source based on areference resonance frequency; a reference cavity; wherein the referencecavity is characterized by the reference resonance frequency; amodulator configured a reference light to generate at least a firstsideband frequency such that an output of said modulator is ameasurement light characterized by at least the first sidebandfrequency; a frequency synthesizer configured to drive the modulator; asecond lock-in mechanism configured to send an electrical signal to thefrequency synthesizer based on a measurement resonance frequency; and ameasurement cavity configured to receive at least a portion of themeasurement light; wherein the measurement cavity is characterized bythe measurement resonance frequency; and wherein the pressure of theenvironment is determined based on the reference resonant frequency andthe measurement resonance frequency. Optionally, a pressure in aninternal volume or in a reference space of the reference cavity is lessthan 0.1 mTorr.

In an aspect, a pressure sensor for determining pressure in anenvironment comprises: a source for emitting a coherent reference lightcharacterized by a reference light frequency; wherein the coherentreference light is further characterized by at least one phasemodulation frequency; an optical splitter for splitting the referencelight into at least a first reference light and a second referencelight; a first lock-in mechanism configured to send an electrical signalto the source based on a reference resonance frequency; a referencecavity configured to receive at least a portion of the first referencelight; wherein the reference cavity is characterized by the referenceresonance frequency; and wherein a pressure within an internal volume orin a reference space of the reference cavity is less than or equal to0.1 mTorr; a modulator configured to receive the second reference lightand modulate the second reference light to generate at least a firstsideband frequency such that an output of said modulator is ameasurement light characterized by at least the first sidebandfrequency; a frequency synthesizer configured to drive the modulator; asecond lock-in mechanism configured to send an electrical signal to thefrequency synthesizer based on a measurement resonance frequency; and ameasurement cavity configured to receive at least a portion of themeasurement light; wherein the measurement cavity is characterized bythe measurement resonance frequency; and wherein the pressure of theenvironment is determined based on the reference resonant frequency andthe measurement resonance frequency.

In an aspect, a method for measuring pressure of an environmentcomprises steps of: introducing the coherent reference light into thereference cavity; providing feedback to the source via the first lock-inmechanism for locking the reference frequency of the reference light tothe reference resonant frequency of the reference cavity; generating thefirst sideband frequency of the measurement light via modulation of thesecond reference light via the modulator; introducing the measurementlight into the measurement cavity; providing feedback to the microwavesynthesizer via the second lock-in mechanism for locking the firstsideband frequency to the measurement resonant frequency of themeasurement cavity; and determining the pressure of the environmentbased on the reference resonance frequency and the measurement referencefrequency.

In another aspect, a pressure sensor for determining pressure in anenvironment comprises: a source for emitting a coherent reference lightcharacterized by a reference light frequency; wherein the coherentreference light is further characterized by at least one phasemodulation frequency; a modulator configured to receive the coherentreference light and modulate the coherent reference light to generate atleast a first sideband frequency and a second sideband frequency suchthat an output of said modulator is a modulated light characterized byat least the first sideband frequency and the second sideband frequency;a frequency synthesizer configured to drive the modulator; an opticalsplitter for splitting the modulated light into at least a firstreference light and a measurement light; a first lock-in mechanismconfigured to send an electrical signal to the source based on areference resonance frequency; a reference cavity configured to receiveat least a portion of the first reference light; wherein the referencecavity is characterized by the reference resonance frequency; andwherein a pressure within an internal volume or in a reference space ofthe reference cavity is less than or equal to 0.1 mTorr; a secondlock-in mechanism configured to send an electrical signal to thefrequency synthesizer based on a measurement resonance frequency; and ameasurement cavity configured to receive at least a portion of themeasurement light; wherein the measurement cavity is characterized bythe measurement resonance frequency; and wherein the pressure of theenvironment is determined based on the reference resonant frequency andthe measurement resonance frequency.

In an aspect, a method for measuring pressure of an environmentcomprises steps of: introducing the coherent reference light to themodulator; generating the first sideband frequency and the secondsideband frequency of the modulated light via modulation of thereference light via the modulator; splitting the modulated light into areference light and a measurement light; introducing the first referencelight into the reference cavity; providing feedback to the source viathe first lock-in mechanism for locking the first sideband frequency ofthe modulated light to the reference resonant frequency of the referencecavity; introducing the measurement light into the measurement cavity;providing feedback to the microwave synthesizer via the second lock-inmechanism for locking the second sideband frequency of the measurementlight to the measurement resonant frequency of the measurement cavity;determining the pressure of the environment based on the referenceresonance frequency and the measurement reference frequency.

In an aspect, a pressure sensor for determining pressure in anenvironment comprises: a first source for emitting a coherent referencelight characterized by a reference light frequency; a first opticalcirculator in optical communication with the first source via an opticalfiber; a second source for emitting a measurement coherent lightcharacterized by a measurement light frequency; a second opticalcirculator in optical communication with the second source via anoptical fiber; a fiber optic coupler in optical communication with thefirst optical circulator via an optical fiber and with the secondoptical circulator via an optical fiber; a reference cavity in opticalcommunication with the fiber optic coupler via an optical fiber andconfigured to receive at least a portion of the coherent reference lightfrom the fiber optic coupler; wherein the reference cavity ischaracterized by the reference resonance frequency; and wherein apressure in a reference space of the reference cavity is less than orequal to 0.1 mTorr; a measurement cavity in optical communication withthe fiber optic coupler via an optical fiber and configured to receiveat least a portion of the measurement light from the fiber opticcoupler; wherein the measurement cavity is characterized by themeasurement resonance frequency; a measurement lock-in mechanism inoptical communication with the first fiber optical circulator via anoptical fiber and configured to send an electrical signal at least tothe second source based on at least the measurement resonance frequency;and a reference lock-in mechanism in optical communication with thesecond fiber optical circulator via an optical fiber and configured tosend an electrical signal at least to the first source based on at leastthe reference resonance frequency; and wherein the pressure of theenvironment is determined based on the reference resonant frequency andthe measurement resonance frequency.

Also disclosed herein are pressure sensors comprising any one or acombination of any of the embodiments of pressure sensors and associatedmethods disclosed herein. Also disclosed herein are methods formeasuring a pressure of an environment comprising any one or acombination of any of the embodiments of pressure sensors and associatedmethods disclosed herein.

Without wishing to be bound by any particular theory, there may bediscussion herein of beliefs or understandings of underlying principlesrelating to the devices and methods disclosed herein. It is recognizedthat regardless of the ultimate correctness of any mechanisticexplanation or hypothesis, an embodiment of the invention cannonetheless be operative and useful.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a schematic of a pressure sensor, according to certainembodiments disclosed herein. FIG. 1B is a schematic illustratingcertain features of the cavity resonances (reference cavity resonanceand measurement cavity resonance) and laser frequencies.

FIG. 2A is a schematic of another pressure sensor, according to certainembodiments disclosed herein. FIG. 2B is a schematic illustratingcertain features of the cavity resonances (reference cavity resonanceand measurement cavity resonance) and laser frequencies.

FIG. 3A is a schematic of another pressure sensor, according to certainembodiments disclosed herein. FIG. 3B is a schematic illustratingcertain features of the cavity resonances (reference cavity resonanceand measurement cavity resonance) and laser frequencies.

FIGS. 4-7 . Each of FIGS. 4-7 is independently a schematic of a pressuresensor for determining pressure in an environment, according to certainembodiments.

FIG. 8 . A schematic illustrating certain features of the referencecavity resonances and the measurement cavity resonances, according tocertain embodiments.

FIGS. 9-12 . Each of FIGS. 9-12 is independently a schematic of apressure sensor for determining pressure in an environment, according tocertain embodiments.

FIG. 13 . A schematic of a small version of a FLOC, as a test ofprinciple. The dimensions can be ˜15 mm on a side. The beam is folded togive a free spectral range of ˜3 GHz, for example.

FIG. 14 . A diagram of an exemplary pressure sensor according to certainembodiments, using a fiber-based cavity with a short section to measurethe refractivity difference between a gas under test and vacuum. Most ofthe cavity is comprised of optical fiber with a short section where theclockwise and counter-clockwise beams travel through free space. Thelong fiber cavity helps the implementation of the sensor by keeping allrequired frequencies low. The cells can be both evacuated, filled withthe same gas, or swapped to test for systematic effects. A similar setupcan be used at high optical power to induce the generation of stimulatedBrillouin scattering leading to narrower laser linewidths andpotentially higher resolution.

FIGS. 15A-15C. A slot waveguide can have >50% of the optical powerpropagating outside the waveguides. FIG. 15A. A schematic top view ofthe ring resonator based on multiple-slot waveguides. FIGS. 15B and 15C.Scanning electron microscope (SEM) images of a silicon nitridemultiple-slot waveguide ring resonator before silicon oxide top claddingdeposition.

FIGS. 16A-16C. Schematics showing exemplary configurations of selectcomponents of pressure sensors, according to certain embodiments of theinvention. FIG. 16A is a pressure sensor configuration includingco-propagating beams and two polarization modes. In the configuration ofFIG. 16A, reference and measurement beams are orthogonally polarized andtravel in the same direction (co-propagating, or same propagation mode).The intracavity optics splits the polarizations and one passes through acell containing the environment (e.g., gas of interest) for measurement.FIG. 16B is a pressure sensor configuration including counterpropagating beams (different propagation direction) and two polarizationmodes. In the configuration of FIG. 16B, reference and measurement beamscan be orthogonally polarized and, as in FIG. 16A, the intra-cavityoptics include two polarization beam displacers to separate andrecombine the beams. FIG. 16C is a pressure sensor configurationincluding counter propagating beams and having the same (parallel) orsimilar polarization mode. In the configuration of FIG. 16C, thereference and measurement beams have parallel polarization but arecounter-propagating with respect to each other. An arrangement similarto that found in polarization independent isolators should do the job.

FIG. 17 . A schematic of an exemplary pressure sensor, according tocertain embodiments. The optical component represented by a circle witha rounded arrow therein is an optical circulator, according to certainembodiments.

FIG. 18A. A perspective view of an exemplary optical cavity, such as ameasurement cavity and/or a reference cavity, according to certainembodiments.

FIG. 18B. A cross-sectional view of the exemplary optical cavity of FIG.18A.

DETAILED DESCRIPTION OF THE INVENTION

In general, the terms and phrases used herein have their art-recognizedmeaning, which can be found by reference to standard texts, journalreferences and contexts known to those skilled in the art. The followingdefinitions are provided to clarify their specific use in the context ofthe invention.

The term “substantially” refers to a property or condition that iswithin 20%, within 10%, within 5%, within 1%, or is equivalent to areference property or condition. The term “substantially equal,”“substantially equivalent,” or “substantially unchanged,” when used inconjunction with a reference value describing a property or condition,refers to a value or condition that is within 20%, within 10%, within5%, within 1%, within 0.1%, or optionally is equivalent to the providedreference value or condition. For example, a frequency offset issubstantially 5 MHz if the frequency offset is within 20%, within 10%,within 5%, within 1%, or equal to 5 MHz. The term “substantiallygreater,” when used in conjunction with a reference value or conditiondescribing a property or condition, refers to a value that is at least2%, at least 5%, at least 10%, or at least 20% greater than the providedreference value or condition. For example, a pressure is substantiallygreater than 1 atm if the pressure is at least 20% greater than, atleast 10% greater than, at least 5% greater than, or at least 1% greaterthan 1 atm. The term “substantially less,” when used in conjunction witha reference value or condition describing a property or condition,refers to a value or condition that is at least 2%, at least 5%, atleast 10%, or at least 20% less than the provided reference value. Forexample, a pressure is substantially less than 1×10⁻⁵ Torr if thepressure is at least 20% less than, at least 10% less than, at least 5%less than, or at least 1% less than 1×10⁻⁵ Torr.

In the following description, numerous specific details of the sensors,systems, mechanisms, devices, device components, and methods of thepresent invention are set forth in order to provide a thoroughexplanation of the precise nature of the invention. It will be apparent,however, to those of skill in the art that the invention can bepracticed without these specific details.

In an aspect, a pressure sensor for determining pressure in anenvironment comprises: a source for emitting a coherent reference lightcharacterized by a reference light frequency; wherein the coherentreference light is further characterized by at least one phasemodulation frequency; an optical splitter for splitting the referencelight into at least a first reference light and a second referencelight; a first lock-in mechanism configured to send an electrical signalto the source (directly or indirectly) based on a reference resonancefrequency; a reference cavity configured to receive at least a portionof the first reference light; wherein the reference cavity ischaracterized by the reference resonance frequency; and wherein apressure within an internal volume or in a reference space of thereference cavity is less than or equal to 0.1 mTorr; a modulatorconfigured to receive the second reference light and modulate the secondreference light to generate at least a first sideband frequency suchthat an output of said modulator is a measurement light characterized byat least the first sideband frequency; a frequency synthesizerconfigured to drive the modulator; a second lock-in mechanism configuredto send an electrical signal to the frequency synthesizer (directly orindirectly) based on a measurement resonance frequency; and ameasurement cavity configured to receive at least a portion of themeasurement light; wherein the measurement cavity is characterized bythe measurement resonance frequency; and wherein the pressure of theenvironment is determined (directly or indirectly) based on thereference resonant frequency and the measurement resonance frequency.

In another aspect, a pressure sensor for determining pressure in anenvironment comprises: a source for emitting a coherent reference lightcharacterized by a reference light frequency; wherein the coherentreference light is further characterized by at least one phasemodulation frequency; a modulator configured to receive the coherentreference light and modulate the coherent reference light to generate atleast a first sideband frequency and a second sideband frequency suchthat an output of said modulator is a modulated light characterized atleast the first sideband frequency and the second sideband frequency; afrequency synthesizer configured to drive the modulator; an opticalsplitter for splitting the modulated light into at least a firstreference light and a measurement light; a first lock-in mechanismconfigured to send an electrical signal to the source (directly orindirectly) based on a reference resonance frequency; a reference cavityconfigured to receive at least a portion of the first reference light;wherein the reference cavity is characterized by the reference resonancefrequency; and wherein a pressure within an internal volume or in areference space of the reference cavity is less than or equal to 0.1mTorr; a second lock-in mechanism configured to send an electricalsignal to the frequency synthesizer (directly or indirectly) based on ameasurement resonance frequency; and a measurement cavity configured toreceive at least a portion of the measurement light; wherein themeasurement cavity is characterized by the measurement resonancefrequency; and wherein the pressure of the environment is determined(directly or indirectly) based on the reference resonant frequency andthe measurement resonance frequency.

In some embodiments, the sensor comprises a processing mechanismconfigured to determine the pressure of the environment (directly orindirectly) based on the reference resonant frequency and themeasurement resonance frequency. In some embodiments, the processingmechanism comprising machine readable instructions to determine thepressure of the environment (directly or indirectly) based on thereference resonant frequency and the measurement resonance frequency. Insome embodiments, the processing mechanism is in electricalcommunication with the frequency synthesizer to determine the pressureof the environment. The processing mechanism may comprise machinereadable instructions (e.g., software). Optionally, the processingmechanism comprises a processor and memory (e.g., a computer).

In some embodiments, the sensor comprises a frequency counter inelectrical communication with the frequency synthesizer; wherein theprocessing mechanism is in electrical communication with the frequencycounter to determine the pressure of the environment.

In some embodiments, the first lock-in mechanism is configured to sendthe electrical signal (directly or indirectly) to the source based on aninterference (“first interference”) of the at least one phase modulationfrequency and the reference resonance frequency. In some embodiments,the first interference is a first beat note corresponding to the atleast one phase modulation frequency and the reference resonancefrequency. In some embodiments, the second lock-in mechanism isconfigured to send the electrical signal to the frequency synthesizer(directly or indirectly) based on an interference (“secondinterference”) of the at least one phase modulation frequency and themeasurement resonance frequency. In some embodiments, the secondinterference is a second beat note corresponding to the at least onephase modulation frequency and the measurement resonance frequency. Insome embodiments, the pressure of the environment is determined(directly or indirectly) based on a comparison of the first interferenceand the second interference.

In some embodiments, the first lock-in mechanism comprises a techniquebased on the Pound-Drever-Hall technique to lock the reference frequencyof the reference light to the reference resonant frequency of thereference cavity; and wherein the second lock-in mechanism comprises atechnique based on the Pound-Drever-Hall technique to lock the firstsideband frequency of the measurement light to the measurement resonantfrequency of the measurement cavity. In some embodiments, the firstlock-in mechanism comprises a technique based on the Pound-Drever-Halltechnique to lock the first sideband frequency of the first referencelight to the reference resonant frequency of the reference cavity; andwherein the second lock-in mechanism comprises a technique based on thePound-Drever-Hall technique to lock the second sideband frequency of themeasurement light to the measurement resonant frequency of themeasurement cavity.

In some embodiments, the first lock-in mechanism is configured to sendthe electrical signal to the source for modulating at least one of thereference light frequency and the phase modulation frequency. In someembodiments, the second lock-in mechanism is configured to send theelectrical signal to the frequency synthesizer for modulating at leastone of the first sideband frequency and the phase modulation frequency.In some embodiments, the second lock-in mechanism is configured to sendthe electrical signal to the frequency synthesizer for modulating atleast one of the second sideband frequency and the phase modulationfrequency.

In some embodiments, the sensor comprises a phase modulator (e.g., errorsignal modulator) to generate the at least one phase modulationfrequency of the reference light. In some embodiments, the error signalmodulator is a phase modulator. In some embodiments, the sensorcomprises an oscillator for driving the phase modulator. In someembodiments, the at least one phase modulation frequency is generatedvia modulation of electrical current to source. In some embodiments, theat least one phase modulation frequency is generated via electricalcurrent modulation of the source. In some embodiments, the at least onephase modulation frequency is characterized by a substantially 5 MHzoffset from the reference light frequency. In some embodiments, the atleast one phase modulation frequency is characterized by an offset fromthe reference light frequency selected from the range of substantially 1MHz to substantially 200 MHz. In some embodiments, the sensor comprisesan oscillator for driving the phase modulator. In some embodiments, atleast one of the first lock-in mechanism and the second lock-inmechanism comprises an error signal generator

In some embodiments, the first lock-in mechanism is configured to sendthe electrical signal to the source indirectly; wherein the firstlock-in mechanism is configured to send the electrical signal to a firstservo, the first servo being configured to modulate the source. In someembodiments, the second lock-in mechanism is configured to send theelectrical signal to the frequency synthesizer indirectly; wherein thesecond lock-in mechanism is configured to send the electrical signal toa second servo, the second servo being configured to modulate thefrequency synthesizer.

In some embodiments, at least one of the first lock-in mechanism and thesecond lock-in mechanism comprises an oscillator for providing afrequency modulation to the at least one of the first lock-in mechanismand the second lock-in mechanism.

In some embodiments, at least one of the first lock-in mechanism and thesecond lock-in mechanism comprises an error signal generator.

In some embodiments, the modulator is selected from the group consistingof an intensity modulator, a phase modulator, an electro-opticmodulator, a Quadrature Phase Shift Keying modulator, and anycombination thereof. In some embodiments, the modulator is selected fromthe group consisting of an intensity modulator, a phase modulator, anelectro-optic modulator, a Quadrature Phase Shift Keying modulator, anacousto-optic modulator, and any combination thereof

In some embodiments, the frequency synthesizer is selected from thegroup consisting of a radio-frequency synthesizer, microwave frequencysynthesizer, a direct digital synthesizer, and a voltage-controlledoscillator.

In some embodiments, the sensor comprises at least one optical detectorconfigured to optically detect the reference resonance frequency and themeasurement resonant frequency. In some embodiments, the sensorcomprises at least one optical detector configured to measure a cavityfrequency difference, the cavity frequency difference being a differencebetween the reference resonant frequency and the measurement resonantfrequency. In some embodiments, the detection of the reference resonancefrequency and the measurement resonant frequency comprises comparingthese to a third optical beam of known frequency, such as via use of afrequency comb stabilized to a microwave frequency reference or a laserstabilized to an atomic or molecular line of known frequency. In someembodiments, the sensor comprises an optical combiner to combine areference cavity light and a measurement cavity light, thereby forming acombined cavity light; wherein the at least one optical detector isconfigured to optically detect the combined cavity light; wherein thereference cavity light is characterized by the reference resonancefrequency and the measurement cavity light is characterized by themeasurement resonance frequency. In some embodiments, the sensorcomprises a frequency counter in electrical communication with the atleast one optical detector and configured to measure a cavity frequencydifference, the cavity frequency difference being a difference betweenthe reference resonant frequency and the measurement resonant frequency.In some embodiments, the cavity frequency difference corresponds to acavity beat frequency corresponding to an interference of the referenceresonant frequency and the measurement resonant frequency; the frequencycounter being configured to determine the cavity beat frequency. Inembodiments, the at least one optical detector is configured to measurethe cavity beat frequency (the beat-note). For example, in embodiments,the at least one optical detector is configured to measure the cavitybeat frequency (the beat-note) and the frequency counter is configuredto measure the cavity frequency difference based on the cavity beatfrequency measurement of the at least one optical detector.

In some embodiments, the modulator is configured to suppress thereference light frequency, such that an intensity at the referencefrequency in the measurement light is less than an intensity at thereference frequency in the second reference light. In some embodiments,the intensity at the reference frequency in the measurement light issubstantially less than or substantially equal to 5% of the intensity atthe reference frequency in the second reference light. In someembodiments, the modulator is configured to suppress the reference lightfrequency, such that an intensity at the reference frequency in themodulated light is less than an intensity at the reference frequency inthe reference light. In some embodiments, the intensity at the referencefrequency in the modulated light is substantially less than orsubstantially equal to 5% of the intensity at the reference frequency inthe reference light.

In some embodiments, at least a portion of a body of each of thereference cavity and the measurement cavity is exposed to the pressureof the environment.

In some embodiments, the pressure within the internal volume of thereference cavity is substantially less than or substantially equal to1×10−5 Torr.

In some embodiments, an offset between the reference frequency and thefirst sideband frequency is selected from the range of 0.1 MHz to 40GHz. This offset may comprise at least one free-spectral-range (FSR) ofthe reference cavity resonance. Further frequency differences can becovered by frequency jumps of 1 FSR. In some embodiments, each of thefirst sideband frequency and the second sideband frequency isindependently characterized by an offset from the reference frequencyselected from the range of 0.1 MHz to 40 GHz. This offset may compriseat least one free-spectral-range (FSR) of the reference cavity resonanceand/or of the measurement cavity resonance.

In some embodiments, an internal volume of the measurement cavitycomprises a gas selected from the group consisting of nitrogen, helium,argon, and any combination thereof; wherein a pressure of the gas issubstantially equal to or substantially greater than 1 atm, oroptionally selected from the range of substantially 1 atm tosubstantially 3 atm. Optionally, the pressure of the gas in the internalvolume of the measurement cavity is less than 1 atm, such as selectedfrom the range of 1 kPa to 100 kPa. Optionally, the pressure of the gasin the internal volume of the measurement cavity is greater than orequal to 1 kPa, optionally selected from the range of 1 kPa to 1 atm, orpreferably in some applications selected from the range of 1 kPa to 3atm. In some embodiments, an internal volume of the measurement cavityis exposed to the environment and pressure within the internal volume ofthe measurement cavity is substantially equivalent to the pressure ofthe environment.

In some embodiments, the source is a diode laser. In some embodiments,the source is characterized by a free running linewidth of less than 1MHz.

In some embodiments, the pressure sensor is configured to measurepressure selected from the range of 1 kPa to 100 kPa with a precisionselected from the range of 3 ppm to 10 ppm.

In some embodiments, the sensor comprises at least one IQ optical hybridfor determining a sign corresponding to the beat frequency, the at leastone IQ optical hybrid being in optical communication with the referencecavity and the measurement cavity.

In some embodiments, each of the reference cavity and the measurementcavity independently comprises an optical contact bond between a mirrorand a resonant body. In some embodiments, each of the reference cavityand the measurement cavity independently comprises an indium seal, asilicate bond, an optical contact bond, or any combination thereofbetween a mirror and a resonant body In some embodiments, each of thereference cavity and the measurement cavity independently comprises aresonator body formed substantially of a material having a bulk modulusgreater than 70 GPa, greater than 90 GPa, greater than 100 GPa, oroptionally greater than 200 GPa. In some embodiments, each of thereference cavity and the measurement cavity independently comprises aresonator body formed of a material selected from the group consistingof sapphire, NEXCERA, AIIVar, Invar, and any combination thereof. Insome embodiments, each of the reference cavity and the measurementcavity independently comprises a resonator body formed of a materialselected from the group consisting of sapphire, ULE, NEXCERA, AIIVar,Invar, and any combination thereof. In some embodiments, each of thereference cavity and the measurement cavity is independentlycharacterized by a cavity length selected from the range ofsubstantially 10 mm to substantially 300 mm, optionally dimensiontherebetween, optionally selected from the range of 10 mm to 50 mm. Insome embodiments, the cavity length of each of the reference cavity andthe measurement cavity is substantially equal to the cavity length ofthe other.

In some embodiments, the sensor comprises a metal sponge in a gas feedline that is operably connected to the reference cavity, the measurementcavity, or both.

In some embodiments, the modulator receives the second reference lightvia an optical fiber. In some embodiments, the modulator receives thereference light via an optical fiber.

In some embodiments, the source and the modulator are in opticalcommunication (directly or indirectly) via at least one optical fiber,the source and the reference cavity are in optical communication(directly or indirectly) via at least one optical fiber, and themodulator and the measurement cavity are in optical communication(directly or indirectly) via at least one optical fiber. In someembodiments, the source, the optical splitter, the firstlock-in-mechanism, the reference cavity, the modulator, the secondlock-in mechanism, and the measurement cavity are in direct or indirectoptical communication with each other via a plurality of optical fibers.

In some embodiments, each of the reference cavity and the measurementcavity is independently characterized by a cavity length that less thanor equal to 15±5 mm. In some embodiments, each of the reference cavityand the measurement cavity is independently characterized by a thermaltime constant of less than 1000 seconds, optionally less than 500seconds, optionally less than 100 seconds. In some embodiments, a timebetween a pressure change and a pressure measurement is less than 100seconds, optionally less than 50 seconds, optionally less than 20seconds. In some embodiments, the pressure sensor is characterized by anintermediate total error of less than or equal to 100±20 ppm. In someembodiments, the intermediate total error corresponds to a precision ofthe pressure measurement. In some embodiments, each of the referencecavity and the measurement cavity is independently characterized by afolded beam path. In some embodiments, the folded beam path is folded atleast twice. For example, the folded beam path can be folded twice usingtwo non-transmitting mirrors to produce a Z-shaped beam path. Forexample, the folded beam path has a ‘Z’-shape. For example, the foldedbeam path includes at least two additional total reflections withrespect to an unfolded straight linear path. In some embodiments, eachof the measurement cavity and the reference cavity is characterized by afree spectral range of less than or equal to 2.4 GHz or of less than orequal to 200 MHz. For example, the free spectral range is less than orequal to 200 MHz for a pressure sensor including a fiber resonator. Forexample, the free spectral range (FSR) can depend on the cavity lengthor light path length in the respective cavity. In some embodiments, thepressure sensor is characterized by a finesse selected from the range of100 to 200,000, optionally 100 to 50,000, optionally 300 to 50,000,optionally 300 to 200,000, optionally less than 350,000. In someembodiments, the frequency synthesizer drives the modulator at afrequency that is less than or equal to half of the free spectral range,optionally less than or within 20% of half of the free spectral range,of each of the measurement cavity and the reference cavity. In someembodiments, each of the measurement cavity and the reference cavity ischaracterized by a mode waist radius selected from the range of 50 μm to500 μm, optionally within 20% of 200 μm. In some embodiments, thereference cavity and the measurement cavity are formed using a resonatorbody and a plurality of mirrors (reflectors); and wherein the mirrorsare characterized by a radius of curvature selected from the range of 1cm to 1 m, optionally 10 cm to 1 m. For example, for a linear cavity,the mirrors can have a radius of curvature of 10 cm. In someembodiments, the reference cavity and the measurement cavity are formedusing a resonator body and a plurality of mirrors (reflectors); andwherein the mirrors are flat. In some embodiments, each of themeasurement cavity and the reference cavity is independently a linearcavity, a folded cavity, or a part of a fiber resonator.

In some embodiments, the pressure sensor comprises at least one fiberresonator, the fiber resonator comprising the reference cavity and themeasurement cavity and the fiber resonator being characterized by thereference resonant frequency and the measurement resonance frequency,respectively. For example, at least a fraction of light in themeasurement cavity and at least a fraction of light in the referencecavity can concurrently occupy the same physical space, but havedifferent light polarization modes or different light propagation(direction) modes with respect to each other. In some embodiments, thereference cavity or the reference resonance frequency corresponds to areference mode of the fiber resonator and the measurement cavity or themeasurement resonance frequency corresponds to a measurement mode of thefiber resonator being. In some embodiments, the reference mode of thefiber resonator and the measurement mode of the fiber resonator arecharacterized by a different light polarization mode with respect toeach other. In some embodiments, the reference mode of the fiberresonator and the measurement mode of the fiber resonator arecharacterized by a different light propagation mode (or, direction oflight propagation) with respect to each other. In some embodiments, atleast a fraction of light in the measurement cavity propagates in adirection that is opposite of a direction propagated by at least afraction of light in the reference cavity. In some embodiments, thefiber resonator comprises a polarization-maintaining optical fiberhaving at least the reference mode and the measurement mode; wherein thereference mode corresponds to a first light polarization mode of thepolarization-maintaining optical fiber and the measurement modecorresponds to a second light polarization mode of thepolarization-maintaining optical fiber. In some embodiments, the fiberresonator comprises a multi-mode optical fiber having at least thereference mode and the measurement mode. In some embodiments, the fiberresonator comprises a multi-mode optical fiber having at least thereference mode and the measurement mode; wherein the reference modecorresponds to a first light propagation mode of the multi-mode opticalfiber and the measurement mode corresponds to a second light propagationmode of the multi-mode optical fiber. In some embodiments, a portion ofthe fiber resonator corresponding to a portion of the measurement cavityis open to the environment, such that light associated with themeasurement cavity in the fiber resonator is exposed to the environment.In some embodiments, a portion of the fiber resonator corresponding to aportion of the reference cavity is open to the reference space, suchthat light associated with the reference cavity in the fiber resonatoris exposed to the reference space; wherein the reference space ischaracterized by a pressure less than or equal to 0.1 mTorr. In someembodiments, the pressure sensor comprises stimulated Brillouinscattering in the fiber resonator.

In some embodiments, the pressure sensor comprises a slot-waveguideresonator; wherein the slot-waveguide resonator comprises a referenceslot following a reference track and a measurement slot following ameasurement track; wherein at least a portion of the reference cavitycorresponds to at least a portion of the reference track and wherein atleast a portion of the measurement cavity corresponds to at least aportion of the measurement track. In some embodiments, each of thereference slot and the measurement slot is independently characterizedby a cross-sectional height selected from the range of 200 to 800 nm anda cross-sectional width selected from the range of 200 nm to 800 nm. Insome embodiments, the reference track corresponds to a Brillouin track,the Brillouin track comprising light from a Brillouin laser. In someembodiments, a temperature of the environment or a temperature of asubstrate of the slot-waveguide resonator is determined based on thepolarization of light in the Brillouin track of the slot-waveguideresonator.

In an aspect, a method for measuring pressure of an environmentcomprises steps of: introducing the coherent reference light into thereference cavity; providing feedback to the source via the first lock-inmechanism for locking the reference frequency of the reference light tothe reference resonant frequency of the reference cavity; generating thefirst sideband frequency of the measurement light via modulation of thesecond reference light via the modulator; introducing the measurementlight into the measurement cavity; providing feedback to the microwavesynthesizer via the second lock-in mechanism for locking the firstsideband frequency to the measurement resonant frequency of themeasurement cavity; and determining the pressure of the environment(directly or indirectly) based on the reference resonance frequency andthe measurement reference frequency.

In an aspect, a method for measuring pressure of an environmentcomprises steps of: introducing the coherent reference light to themodulator; generating the first sideband frequency and the secondsideband frequency of the modulated light via modulation of thereference light via the modulator; splitting the modulated light into areference light and a measurement light; introducing the first referencelight into the reference cavity; providing feedback to the source viathe first lock-in mechanism for locking the first sideband frequency ofthe modulated light to the reference resonant frequency of the referencecavity; introducing the measurement light into the measurement cavity;providing feedback to the microwave synthesizer via the second lock-inmechanism for locking the second sideband frequency of the measurementlight to the measurement resonant frequency of the measurement cavity;determining the pressure of the environment (directly or indirectly)based on the reference resonance frequency and the measurement referencefrequency.

In some embodiments, prior to the step of determining, the methodfurther comprising combining a reference resonant light from thereference cavity and the measurement resonant light from the measurementcavity to form a combined resonance light; wherein the referenceresonant light is characterized by the reference resonant frequency, themeasurement resonant light is characterized by the measurement resonancefrequency, and the combined resonant light is characterized by a beatfrequency corresponding to the combination of the reference resonantfrequency and the measurement resonant frequency. In some embodiments,the method comprises optically detecting a combined resonance light. Insome embodiments, the step of optically detecting comprises detecting abeat resonance frequency in the combined resonance light; the beatresonance frequency corresponding to a convolution of the referenceresonance frequency and the measurement resonance frequency. In someembodiments, the step of determining comprises determining the pressureof the environment (directly or indirectly) based on the beat resonancefrequency. In some embodiments, the method comprises phase modulatingthe reference light to generate the at least one error signal sideband.In some embodiments, the step of determining comprising determining thepressure of the environment (directly or indirectly) based on acomparison of a first beat note and a second beat note; wherein thefirst beat note corresponds to a convolution of an error signal sidebandand the reference cavity frequency; and wherein the second beat notecorresponds to a convolution of an error signal sideband and themeasurement cavity frequency. In some embodiments, the method furthercomprises determining a temperature of the environment.

In an aspect, a pressure sensor for determining pressure in anenvironment comprises: a first source for emitting a coherent referencelight characterized by a reference light frequency; a first opticalcirculator in optical communication with the first source via an opticalfiber; a second source for emitting a measurement coherent lightcharacterized by a measurement light frequency; a second opticalcirculator in optical communication with the second source via anoptical fiber; a fiber optic coupler in optical communication with thefirst optical circulator via an optical fiber and with the secondoptical circulator via an optical fiber; a reference cavity in opticalcommunication with the fiber optic coupler via an optical fiber andconfigured to receive at least a portion of the coherent reference lightfrom the fiber optic coupler; wherein the reference cavity ischaracterized by the reference resonance frequency; and wherein apressure in a reference space of the reference cavity is less than orequal to 0.1 mTorr; a measurement cavity in optical communication withthe fiber optic coupler via an optical fiber and configured to receiveat least a portion of the measurement light from the fiber opticcoupler; wherein the measurement cavity is characterized by themeasurement resonance frequency; a measurement lock-in mechanism inoptical communication with the first fiber optical circulator via anoptical fiber and configured to send an electrical signal at least tothe second source based on at least the measurement resonance frequency;and a reference lock-in mechanism in optical communication with thesecond fiber optical circulator via an optical fiber and configured tosend an electrical signal at least to the first source based on at leastthe reference resonance frequency; and wherein the pressure of theenvironment is determined based on the reference resonant frequency andthe measurement resonance frequency, optionally the difference betweenthe reference resonant frequency and the measurement resonancefrequency. For example, this pressure sensor with optical fibers can bemore compact than conventional systems.

In some embodiments, the measurement lock-in mechanism is in electricalcommunication with a processing mechanism configured to determine thepressure of the environment based on the reference resonant frequencyand the measurement resonance frequency, optionally the differencebetween the reference resonant frequency and the measurement resonancefrequency.

In some embodiments, the measurement lock-in mechanism comprises a firstoptical detector and a first error signal modulator, wherein the firstoptical detector is in electrical communication with the first errorsignal modulator and the first error signal modulator is in electricalcommunication with the second source. In some embodiments, the referencelock-in mechanism comprises a second optical detector and a second errorsignal modulator, wherein the second optical detector is in electricalcommunication with the second error signal modulator and the seconderror signal modulator is in electrical communication with the firstsource.

In some embodiments, the reference coherent light is characterized by afirst at least one phase modulation frequency and wherein the firsterror signal modulator generates the first at least one phase modulationfrequency of the measurement light. In some embodiments, the measurementlight is characterized by a second at least one phase modulationfrequency and wherein the second error signal modulator generates thesecond at least one phase modulation frequency of the reference coherentlight.

In some embodiments, the reference cavity and the measurement cavity areformed using a resonator body and a plurality of mirrors; and whereinthe mirrors are characterized by a radius of curvature selected from therange of 1 cm to 1 m, optionally 10 cm to 1 m. In some embodiments, thepressure sensor comprises at least one fiber resonator, the fiberresonator comprising the reference cavity and the measurement cavity andthe fiber resonator being characterized by the reference resonantfrequency and the measurement resonance frequency, respectively. In someembodiments, the reference cavity or the reference resonance frequencycorresponds to a reference mode of the fiber resonator and themeasurement cavity or the measurement resonance frequency corresponds toa measurement mode of the fiber resonator being. In some embodiments,the reference mode of the fiber resonator and the measurement mode ofthe fiber resonator are characterized by a different light polarizationmode with respect to each other. In some embodiments, the reference modeof the fiber resonator and the measurement mode of the fiber resonatorare characterized by a different light propagation (direction) mode withrespect to each other. In some embodiments, at least a fraction of lightin the measurement cavity propagates in a direction that is opposite ofa direction propagated by at least a fraction of light in the referencecavity. In some embodiments, the fiber resonator comprises apolarization-maintaining optical fiber having at least the referencemode and the measurement mode; wherein the reference mode corresponds toa first light polarization mode of the polarization-maintaining opticalfiber and the measurement mode corresponds to a second lightpolarization mode of the polarization-maintaining optical fiber. In someembodiments, the fiber resonator comprises a multi-mode optical fiberhaving at least the reference mode and the measurement mode; wherein thereference mode corresponds to a first light propagation mode of themulti-mode optical fiber and the measurement mode corresponds to asecond light propagation mode of the multi-mode optical fiber. In someembodiments, a portion of the fiber resonator corresponding to a portionof the measurement cavity is open to the environment, such that lightassociated with the measurement cavity in the fiber resonator is exposedto the environment. In some embodiments, a portion of the fiberresonator corresponding to a portion of the reference cavity is open tothe reference space, such that light associated with the referencecavity in the fiber resonator is exposed to the reference space; whereinthe reference space is characterized by a pressure less than or equal to0.1 mTorr. In some embodiments, the pressure sensor comprises stimulatedBrillouin scattering in the fiber resonator. In some embodiments, thereference cavity and the measurement cavity are in optical communicationwith at least one beam displacer configured to displace light based onits polarization. In some embodiments, the reference cavity and themeasurement cavity are in optical communication with at least onehalf-wave plate. In some embodiments, each of the at least one beamdisplacer combines light associated with the reference cavity with lightassociated with the measurement cavity. See also FIGS. 16A-16B for someexemplary configurations including beam displacer(s).

In some embodiments, the first source is a pump laser.

In some embodiments, each of the reference cavity and the measurementcavity is independently characterized by a thermal time constant of lessthan 1000 seconds, optionally less than 500 seconds, optionally lessthan 100 seconds. In some embodiments, a time between a pressure changeand a pressure measurement is less than 100 seconds, optionally lessthan 50 seconds, optionally less than 20 seconds. In some embodiments,the pressure sensor is characterized by an intermediate total error ofless than or equal to 100±20 ppm. In some embodiments, the intermediatetotal error corresponds to a precision of the pressure measurement. Insome embodiments, each of the measurement cavity and the referencecavity is characterized by a free spectral range of less than or equalto 2.4 GHz or of less than or equal to 200 MHz. For example, the freespectral range is less than or equal to 200 MHz for a pressure sensorincluding a fiber resonator. For example, the free spectral range (FSR)can depend on the cavity length or light path length in the respectivecavity. In some embodiments, the pressure sensor is characterized by afinesse selected from the range of 100 to 200,000, optionally 100 to50,000, optionally 300 to 50,000, optionally 300 to 200,000, optionallyless than 350,000. In some embodiments, the frequency synthesizer drivesthe modulator at a frequency that is less than or equal to half of thefree spectral range, optionally less than or within 20% of half of thefree spectral range, of each of the measurement cavity and the referencecavity. In some embodiments, each of the measurement cavity and thereference cavity is characterized by a mode waist radius selected fromthe range of 50 μm to 500 μm, optionally within 20% of 200 μm.

The invention can be understood by the following non-limiting examples.

Example 1

FIG. 1A is a schematic of a pressure sensor, according to certainembodiments disclosed herein. In FIG. 1A, each of “ILS” and “ILS*”independently refers to an “integrated laser system.” In someembodiments, the terms “ILS” or “integrated laser system” may be usedinterchangeably with the term “lock-in mechanism,” and vice versa. Eachone of the ILSs performs signal demodulation and servo feedback to keepthe laser frequency locked to the respective cavity resonance. The ILSfor the measurement cavity has been modified to be phase-locked to theILS for the reference cavity, allowing it to demodulate thePound-Drever-Hall (PDH) sidebands with the appropriate phase. FIG. 1B isa schematic illustrating certain features of the cavity resonances(reference cavity resonance and measurement cavity resonance) and laserfrequencies.

Described in this example is a photonic pressure sensor, according tocertain embodiments, that provides a various advantages with respect tothe sensor described Egan, et al. (Egan, Patrick F., Jack A. Stone, JayH. Hendricks, Jacob E. Ricker, Gregory E. Scace, and Gregory F. Strouse.“Performance of a dual Fabry-Perot cavity refractometer.” Optics letters40, no. 17 (2015): 3945-3948), which is incorporated herein by referenceto the extent not inconsistent herewith. The pressure sensor relies onthe change in refractive index as a function of pressure. The indexchange causes an optical path length change, leading to a shift of theresonant frequency of a cavity formed by two mirrors attached to anultra-low expansion glass (ULE) spacer. In Egan, et al., two opticalcavities are formed in a common ULE spacer. One by drilling a borethrough the spacer and attaching mirrors to the spacer. The other cavityis formed by drilling a channel which is ultimately exposed to theenvironmental conditions outside the spacer. Mirrors are also attachedto form this cavity. A laser can be locked to each of these cavities.The most common method for locking a laser to a cavity resonance isknown as Pound-Drever-Hall locking, which is further described in Black(Black, Eric D. “An introduction to Pound-Drever-Hall laser frequencystabilization.” American Journal of Physics 69, no. 1 (2001): 79-87),which is incorporated herein by reference to the extent not inconsistentherewith.

Several advantages are achieved herein over the implementation in Egan,et al. by using laser modulation techniques allowing us to produce asensor with smaller foot-print, weight, power consumption as well aslower cost and system complexity. First, instead of using bulky gaslasers as in Egan, et al., we use a diode laser significantly reducingthe power consumption and the footprint of the system. Second, insteadof detecting a beat-note between two lasers locked to each the referenceand measurement cavities, we split a portion off the diode laser and usean electro-optic modulator to generate a sideband which is subsequentlylocked to the measurement cavity. The advantage of doing this is atleast two-fold: 1) it halves the laser count in the system and, 2) itobviates the need to detect a beat frequency between the two laserssince the sideband offset frequency is given by the synthesizerfrequency. In some embodiments, an off-the-shelf frequency synthesizeris used and a small fraction of the power is split off before drivingthe modulator and measured using a frequency counter. This gives astraightforward, high signal-to-noise ratio signal to count—somethingwhich isn't always straightforward to obtain from an optical beat-note.In some embodiments, the synthesizer may be replaced for a directdigital synthesizer (DDS) which may further simplify the setup byobviating the need for a frequency counter, as the digital tuning wordfor the synthesizer directly gives a reading of the frequency offset.

One challenge is that one must determine whether it is the uppersideband or the lower sideband which is locked to the measurementcavity. This challenge also exists in the implementation in Egan, etal., in the form of a beat-note sign determination. The second challengeis particular to the sideband locking case and it arises when the offsetfrequency is equal to one-half of the free-spectral range of themeasurement cavity in that case both sidebands become resonant withseparate cavity resonances, causing signal interference. Thesechallenges can be addressed via any one or more of the followingembodiments:

-   -   1) an acousto-optic modulator can be inserted in the measurement        arm. By introducing a small shift with known sign, the change in        the synthesizer frequency to maintain the lock will disambiguate        whether it is the upper or lower sideband which is locked to the        measurement cavity. Also, the introduction of a frequency shift        eliminates the second problem by effectively shifting the        carrier away.    -   2) The intensity modulator can be replaced for a quadrature        phase-shift keying (QPSK) modulator, which can allow one to        generate a single-sideband with carrier suppressed, effectively        eliminating both problems. An apparent problem that may arise        when the measurement and reference resonances overlap is        addressed by keeping the offset frequency >1 FSR away.    -   3) The intensity modulator can be replaced by a phase modulator        and the optical frequency shift can be directly generated by the        DDS by summing a serrodyne function to the sideband-generating        function. The sign can then be determined as in point 1). The        introduction of serrodyne modulation can also solve the second        challenge in the same way as 1).    -   4) If a beat-note is being detected, an optical IQ hybrid can be        used to determine the sign. This embodiment can be combined with        one or more of the above embodiments to solve the second        challenge.

Examples 2-11

The pressure sensors, and associated methods, described in theseexamples provide various advantages over conventional systems such asthose described in Egan, et al. and in Hendricks, et al. (U.S. Pat. No.9,719,878), which is incorporated herein by reference to the extent notinconsistent herewith.

The sensors described herein can be useful as a transfer standardbecause the measurement accuracy can be largely derived from the atomicproperties of nitrogen. This method is also useful for precisemeasurements of pressure, such as in the 10 kPa range, whereconventional sensors are wanting.

The pressure sensors, and associated methods, described herein may bereferred to as dual Fabry-Perot (FP) photonic pressure sensors.Generally, these sensors compare the resonant frequencies between twomedium-finesse FP cavities: a reference cavity with its beam pathevacuated to vacuum pressure, and a second test cavity with its beampath filled with nitrogen at the pressure to be measured. Thefrequencies of two lasers are referenced to the effective lengths of thetwo cavities with precision servo locking to the same or similar modeorder (number of wavelengths in a round trip of the cavity). Any changein the pressure of the test cavity gas changes the gas's refractiveindex, and correspondingly the effective length and hence the frequencyof the laser locked to it. The frequency of the reference laser remainsunchanged, to first order. As a result, the beat frequency between thetwo lasers is a readout of the differential gas pressure, whencorrection terms are applied to account for non-ideal gas behavior andcavity distortion. In some embodiments, the sensors described herein arefield-ready, portable, transportable, and robust without sacrificingperformance.

In some embodiments, the sensors described herein provide ultra-highprecision (3 ppm to 10 ppm) and traceable pressure measurements in aportable, cost-effective package. In some embodiments, the sensors arecharacterized by reduced SWaP-C with respect to conventional approaches(e.g., Egan, et al.) for robust operation in a field environment.

Example 2

Certain conventional systems use two He—Ne lasers. These lasers arecostly and bulky and have limited lifetime. In contrast, according tosome embodiments, the systems described herein use two semiconductorlasers or one semiconductor laser and an advanced modulation scheme.Semiconductor lasers are compact, power efficient, and inexpensive. Theyhave a predictable frequency tuning curve as a function of temperatureand current. Using commercially available temperature and currentcontrol, the laser frequency can be predicted to <1 GHz. This allowsknowledge of the mode difference number in combination with coarsepressure gauge data. The particular diode laser type to be used will bea crucial part of this device. Diode lasers have the advantage of beinginexpensive and tunable in frequency (through changing the diode biascurrent or device temperature. The critical parameter is the freerunning linewidth (preferred <1 MHz), and the Fourier frequency at whichthe response is 90 degrees delayed in phase from an applied modulationfrequency. This latter quantity determines to what extent electronicfeedback can control the linewidth of the laser under servo control. Thelaser unit price is also a consideration for some of the devicesenvisioned. Some lasers have a strong frequency selection device (Braggreflector), for example RIO. These lasers have free running linewidthsof ˜25 kHz, though may exhibit non-smooth frequency tuning over GHz offrequency range. The price is at the $5k level, which is acceptable fora high-end transfer pressure standard though not a device for processpressure measurement. SLS is characterizing Denselight laser sources,which are inexpensive and have a linewidth of ˜100 kHz. NEL lasers areinexpensive, though the cavity resonance with would have to be >=1 MHzfor effective locking.

Example 3

According to some embodiments, the systems described herein use advancedmodulation schemes to use a single laser to interrogate both cavities.This also simplifies the beat frequency measurement, compared to usingtwo lasers, as the beat frequency can be determined by appliedmodulation frequency (e.g., tuning word in DDS) rather than usingGHz-bandwidth detectors and divider electronics to bring the beat signalto a frequency that can be digitized.

Example 4

Certain conventional approaches use a third absolute frequency referenceto determine the sign of the beat frequency between the reference andmeasurement lasers. In contrast, according to some embodiments, thesystems described herein use of IQ optical hybrids to determine the signof the beat-note (or, cavity beat frequency). Alternatively, we coulduse a phase of dither applied to one laser as means to determine sign ofbeat-note.

Example 5

Certain conventional systems use mirrors that are bonded using asilicate bonding process, and this process has been shown to produceinconsistent bonding creeps. For example, this can lead to non-commonmode frequency drift of the reference and measurement cavities—degradinguncertainty of the sensor. In contrast, according to some embodiments,the systems described herein use optical contacting for bonding withreduced contact drift.

Example 6

Some conventional systems (e.g., Egan, et al.) use a settling time of˜90 minutes. In contrast, according to some embodiments, the systemsdescribed herein include improved thermal properties of the cavitycomponents (e.g., resonant body, spacer) that lead to shorter settlingtimes for continuous measurements.

Example 7

Certain conventional systems use a ULE spacer in the cavity, which has abulk modulus of 70 GPa. The bulk modulus determines the amount ofdeformation endured by the cavity when brought up to pressure. Incontrast, according to some embodiments, the systems described hereinuse larger bulk modulus materials, such as but not limited to, Sapphire,NEXCERA or AIIVar, for reduced deformation coefficients. Table 1compares properties of certain materials.

TABLE 1 Property ULE Sapphire NEXCERA CTE <10⁻¹⁰ K⁻¹ 9e−6 <10⁻¹⁰ K⁻¹(slope: 1.1 × 10⁻⁹ K⁻²) (slope 4.9 ×10⁻⁹ K⁻²) Young's 68 GPa 345 GPa 130GPa modulus Bulk 34 GPa 241 GPa modulus

Example 8

Certain conventional systems use a 150 mm long cavity. In contrast,according to some embodiments, the systems described herein use smallercavity lengths to reduce cost and improve portability. This mayconventionally lead to the problem of having to count higher beatfrequencies. However, the sensors and methods described here havingadvanced modulation schemes simplify the frequency measurement processsignificantly (specifically is a DDS is used to generate the laser tointerrogate the measurement cavity). In some embodiments, 50 mm cavitiesare used. This has the added benefit of reducing the mode numberdifference that needs to be tracked in a large dynamic rangemeasurement.

Example 9

Certain conventional systems, require filling the sample gas directly toan evacuated chamber for each measurement. This leads to a large amountof enthalpy heat released onto the cavity spacer which has to bethermalized over the 90 minutes stated above. In contrast, according tosome embodiments, the systems described herein use a metal sponge in thefeed line to pre-condition the sample and absorb the enthalpy energyfrom the free expansion of the fill gas in to the low-pressure chambervolume.

Example 10

According to some embodiments, the sensors described herein use apliable vacuum seal to keep the reference cavity evacuated. An Indiumseal can be used to better preserve the cavity dimensional stability.

Example 11

Certain conventional systems rely on free-space optics to couple intocavity, which makes it an instrument for the laboratory environment. Incontrast, according to some embodiments, the systems described hereinuse mostly fiber-optic components to improve the instrument'sportability and robustness. Additionally, hybrid isolators and splittersto reduce the size and cost of the final instrument. Mode-matchingoptics from fiber to cavity can be integrated/glued to the vacuumhousing. Alignment can be done quickly with high-efficiency coupling toTEM00. This assembly has been shown to be robust in commercial transportand to operate in field environments.

Additional Examples

Each of FIGS. 2-7 and 9-12 is independently a schematic corresponding toan exemplary pressure sensor, according to certain embodiments of theinvention. Solid and dashed lines represent communication betweencomponents connected by said lines. Generally, though not necessarily,the solid lines represent optical communication (or, optical coupling)between components, such as via optical fiber through which lightpasses. Generally, though not necessarily, the dashed lines representelectrical communication, which allows for transfer of electricalsignals between the connected components. Each of the exemplary pressuresensors of FIGS. 2-7 and 9-12 independently comprises one or more of thefollowing components or features: a source of light (e.g., laser diode)102; a beam splitter 104; a beam splitter 106; a first lock-in mechanism108, which in some embodiments is or comprises an error signal generatorby coherent demodulation (PDH error signal), and which can, in someembodiments, comprise a servo and/or an oscillator; a reference cavity110; a gas or vacuum line 112; a pump 114; a modulator 116, which insome embodiments is an intensity modulator, a phase modulator, a QPSKmodulator, and/or an electro-optic modulator; a frequency synthesizer118, which in some embodiments is a radio frequency synthesizer or adirect digital synthesizer; an optical circulator 120; a second lock-inmechanism 122, which in some embodiments is an error signal generator bycoherent demodulation (PDH error signal); a measurement cavity 124; agas feed line 126; a gas source or environment 128; an optical combiner130; an optical detector 132; a frequency counter 134; a processingsystem 136; a block, body, or support for at least one cavity 138; aphase modulator 140; a servo 142; an oscillator 144; a servo 146; anoptical coupler or a beam splitter 148; an optical coupler or a beamsplitter 150; a frequency counter 152; and a processing mechanism 154.Optionally, optical communication paths (represented by certain lines)are identified as comprising one or more of the following light (or,optical signals): a coherent reference light 101, which is phasemodulated in some embodiments; a first reference light 103; a secondreference light 105; a measurement light 107; a reference resonancelight 115; a measurement resonance light 117; and a combined resonancelight 119. A lock-in mechanism (e.g., 108 and/or 122) can optionallycomprise an optical detector. It is also noted that additionaldescription of certain exemplary optical cavities, their components, andother components, and methods of forming any of these, may be describedin, for example, Notcutt, et al. (U.S. Pat. No. 10,141,712),Plusquellic, et al. (U.S. Pat. No. 8,642,982), and Silander, et al.[Silander, Isak, Martin Zelan, Ove Axner, Fredrik Arrhen, LesliePendrill, and Aleksandra Foltynowicz. “Optical measurement of the gasnumber density in a Fabry-Perot cavity.” Measurement Science andTechnology 24, no. 10 (2013): 105207], all of which are incorporatedherein by reference to the extent not inconsistent herewith, as well asin Hendricks, et al. and Egan, et al.

Example 12: Making Dual Fabry-Perot Pressure Sensors Inexpensive and forWide Application

NIST developed a dual Fabry-Perot (FP) cavity pressure sensing device(acronym FLOC=fixed length optical cavity) with many advantages oversome previous technologies [1,2]. In this Example, the presentlydisclosed dual Fabry-Perot cavity pressure sensing technology, accordingto some embodiments, is less costly to manufacture, and smaller inphysical size than previous devices. The smaller sensors of this Exampleare designed towards thermal time constants of tens of seconds and canhave intermediate total error values (say 100 ppm).

Pressure sensing is a >$8 bn dollar market with remarkable breadth, fromaviation to process control. These dual FP pressure sensors are likelyto start at the precision, high price-point end of the market, forexample, a transfer standard for calibration. How their applicationdiffuses from this end of the market and where their niche may be willdepend to some extent on how low cost they can be made. An example isaccurate pressure measurement for cavity ringdown spectrometers.

For example, the sensors disclosed here, according to certainembodiments, include medium finesse Fabry-Perot cavities. The widedeployment of fiber optics has made FP optical filters widespread,though the ITU grid has separations at the 50 GHz level. The level ofprecision of these sensors disclosed here, according to certainembodiments, can be MHz or less. This is a step forward for opticalsensing and enables deployment of further sensing technologies. The useof a laser locked to a micro-optic FP cavity optical assembly is a pushinto new territory for the way FPs are built and sensors are made.

These pressure sensors can be moved to photonic integrated chip (PIC)platforms. This is the way forward for optical sensors where cost is theparamount driver, for example in laser radar in cars. PIC technology isalso the thrust of some DARPA programs, and some of the most successfulPIC devices developed to date are Brillouin lasers. A problem in a PICapproach is that it is difficult to have an approximately zero thermalexpansion coefficient reference cavity in vacuum, which is part of theexisting NIST FLOC approach. It is also difficult to have a fullyfree-space cavity for sensing the gas. For the reference cavity, thechallenge is work around the temperature dependence of dn/dT˜10⁻⁵ K⁻¹.This is some four orders of magnitude larger than the thermal expansioncoefficient of Corning 7973 ultra-low expansion (ULE) glass, which canbe as low as 10⁻⁹ K⁻¹. The second challenge is to decouple the sensecavity from the waveguide, to allow the light to sufficiently feel therefractive index of the gas to be measured. These challenges areaddressed by the pressure sensors disclosed here, according to certainembodiments, thereby providing for precision pressure sensors with lowsize, weight, power and cost that are made with a semiconductor process.

Some challenges, constraints, or technical questions considered and/oraddressed in this Example include: The creep of such a structure.Decrease in curved mirror size while still optically contacting at theannulus. Size vs complexity, given the constraints that the speed of theelectronics should remain in the few GHz range. Using silicate/hydroxidebonded joints that are thin enough that bond-length creep is acceptablysmall, which helps remove requirement for polishing the surfaces foroptical contact, reducing cost and allowing smaller curved mirrors to beused (as no polished annulus is required). Use of a getter pump or novelsmall ion pump. Temperature and ramp profiles are considered for bakingthe cavity to get rid of volatiles to reduce loading on the pump.

Some pressure sensors disclosed here use a fiber ring cavity using afour port circulator to introduce the two short, independent paths wherethe sample and reference would be located. See for example FIG. 17 .Some pressure sensors disclosed here use a Brillouin laser approachwould improve the sensor performance. Some pressure sensors disclosedhere use integrated optics sensor. Some pressure sensors disclosed hereuse counter-propagating beams in the fiber case.

Some pressure sensors disclosed here use miniature conventionalcavities, such as shown in FIG. 13 .

The benefits of shrinking the cavity include: the material costsdecrease, the volume of the instrument decreases; thermal time constantsdecrease, and temperature gradients decrease. What becomes moredifficult in the shrinking process is: The free spectral range FSR=c/2 Lincreases, possibly to >6 GHz. This makes signal electronics exotic,complex, costly, and power hungry; If optical contacting is to be usedto bond the mirrors, then polishing an annulus on a mirror of smalldiameter becomes difficult.

The cavity configuration of FIG. 13 has a folded beam path, to keep theFSR and the signal electronics to a manageable frequency. Some pressuresensors disclosed here use direct digital synthesis (DDS) frequencies of1.2 GHz at the moment. This 1.2 GHz can be half a free spectral range.With an FSR of 2.4 GHz, and with a beam that is folded twice, this wouldgive a cavity length or a cavity spacer edge length of ˜15 mm. There isan increase in complexity through the number of surfaces that arepolished, two different optical coatings are needed, additional opticalcontacts, and machining tolerances, though all of these are routine inoptical fabrication. A folded cavity has distinct non-degenerate modesfor S and P polarizations, so one can couple into the cavity using onlyone polarization (S).

Some pressure sensors disclosed here use optical contacting to bond themirrors to the spacer. Many FP cavities use this (some with 5×10⁻¹⁷fractional stability at 1 s), and laser gyros use this (including thebond as a vacuum seal). Optical contacting of curved mirrors requires aflat annulus polished at the rim. This annulus can be a few mm wide, andthere will likely be some damage to the surface near the annulus (as itis generally polished after the mirror surface). The mode diameter maybe of order 200 um, though it is apparent that it is difficult tocontact mirrors of small diameter. For example, some pressure sensorsdisclosed here use reflectors with 10 cm radius of curvature, 7.75 mmdiameter mirrors.

Some pressure sensors disclosed here use hydroxide bonding to bondmirrors to the spacer. These can have an exponential frequency changeequivalent to a bond shrinkage of ˜100 nm. Some pressure sensorsdisclosed here use a thinner bond, such as by applying a clamping force,to reduce the bond length change to an acceptable level, allowing forsmaller mirrors to be used.

Vacuum is used in the reference cavity, and for a commercial product ina regular commercial environment, it may have to come back to life aftera period of being switched off. Some pressure sensors disclosed here usea small ion pump, optionally if the outgassing rate of the cavity volumeis sufficiently low. The cavity can be baked at a few hundred C to getrid of volatiles. Some pressure sensors disclosed here use cavitiesbakes at 80° C., though the effect on cavity drift can be not uniform atthis temperature. Some pressure sensors disclosed here use cavitiesbakes at ˜400° C., optionally under high vacuum. Drift is consideredbecause too large a drift would compromise the device accuracy.

Some pressure sensors disclosed here use a non-evaporable getter pumpmay suffice if Helium is not an issue. Some pressure sensors disclosedhere have a finesse of >500,000 to ˜350,000, optionally ˜50,000

One further consideration is the optical design. Fiber optics areinexpensive and have a plug-and-play convenience. Bend-insensitive fibercan be used to improve how compactly the parts can be packaged, thoughthe requirements for splicing make free space micro-optics a morecompact approach for some beam paths.

Some pressure sensors disclosed here use nitrogen or argon (e.g., gasesfor which the refractive index ratio to that of helium has beenmeasured). Some pressure sensors disclosed here use a differential gaugeplaced between the dual FP sensor using nitrogen and the gas ofinterest.

Some pressure sensors disclosed here use a version of Egan and Stone[16] in which the laser is frequency stabilized to rubidium in aquasi-monolithic structure [15]. There are consideration of therequirements for frequency doubling from 1556 nm, or using 778 nm, whichwould require a measurement of the refractive index.

The NIST photonic pressure sensor is essentially a refractometer,linking the gas pressure measurement directly to a frequency measurementof a resonant cavity. This allows one to access the level of precisionafforded by frequency counting. The mode in the FLOC sensor lives onlyin either vacuum or the gas whose refractivity is to be measured. Usingintegrated photonics approaches at least partially changes this, forcingthe optical mode to be guided in some type of waveguide. Some pressuresensors disclosed here use two modes in a single waveguide to obtain asignificant amount of common-mode rejection of the shifts induced by theresonator's length and index changes as a function of temperature andother environmental perturbations.

The second challenge was already addressed above regarding theminiaturization of the standard cavity approach, and it is related tothe increase in free-spectral-range for smaller resonators. This problemdoes not affect the performance of the sensor, instead, it increases thecost of the final product by necessitating higher frequency signals andcomponents. However, integrated photonics of some of the pressuresensors disclosed here use can provide a path to mitigate the problem ofhigh free-spectral-range in smaller resonators by using long delay linesin waveguides such as spiral resonators.

Some pressure sensors disclosed here use fiber resonators. For example,an optical fiber can be wound in a small package to obtain cavities withlow free-spectral-range, in the range of 200 MHz or less. At the sametime, a small region of the cavity can be made to travel throughfree-space to interact with the gas under test. To obtain goodsuppression of the fiber drifts, two modes in the same fiber can beused. Possibilities include two polarizations in one fiber or twocounter-propagating modes in a fiber loop. The first option allows for asimple implementation by using a short free-space section where the twopolarizations travel through different paths, one sampling the gas ofinterest and the other sampling a reference path. The second option hasthe advantage that it avoids the differential thermo-optic coefficientsbetween the two orthogonal polarizations in fiber. In this case, thedegeneracy between these two modes can be lifted in the free-spaceregion as well, by using polarization optics akin to those insideoptical isolators, such as shown in FIG. 14 or FIG. 17 , for example. Inthis way, the two counter-propagating cavities can be made to share allthe same components except for the gas under test. Additionalimprovements to this approach can use stimulated Brillouin scattering inthe fiber to further reduce the linewidth of the sensing laser.Interestingly, if Brillouin scattering is used, the first and secondorder Stokes waves can be used to sample the co- and counter-propagatingpaths with a single pump laser.

For example, in the exemplary pressure sensor configuration of FIG. 14 ,the first (left) circulator (i) receives reference light from the “pumplaser” and sends it to the “optical coupler”, and (ii) receives lightfrom the measurement cavity via the optical coupler and sends that tothe measurement (bottom) lock-in mechanism. For example, in theexemplary pressure sensor configuration of FIG. 14 , the second (right)circulator (i) receives measurement light from the “measurement laser”and sends it to the “optical coupler”, and (ii) receives light from thereference cavity via the “optical coupler” and sends that to thereference (top) lock-in mechanism. For example, in the exemplarypressure sensor configuration of FIG. 14 , the reference (“Ref.”) lightsource can be a pump laser. For example, in the exemplary pressuresensor configuration of FIG. 14 , the measurement light source can be alaser.

Some pressure sensors disclosed here use a slot-waveguide PIC resonatorcan have >50% of the optical power propagating outside the waveguide[16]. The slot waveguide can have a form of compensation for the dn/dTcontribution to frequency change. This can be a Brilloun laser racetrackthat is laid out next to the slot waveguide racetrack. The differentialresponse of the two polarizations in a Brillouin laser can be used toread out the temperature of the substrate (assuming distances are smalland gradients are small enough) [6].

The refractive index of helium can be calculated. Measurement of theratio of the refractive index of the sense gas (nitrogen or argon) toHelium have been published by Egan [12] and others [13].

Some pressure sensors disclosed here use whispering gallery mode devices(PIC, Si or MgF or CaF disc) can have differential responses totemperature for different modes, either through different polarization[6] or different mode number [5]. The former could be attractive as asource of stable reference light. The latter is potentially useful for alower sensitivity device: the exposure of the mode to the gas to bemeasured is low. The integrated photonics stabilization of lasers to Rb[14] also provides a path forward to a frequency stabilized laser in anintegrated environment.

REFERENCES

-   [1] Patrick F Egan et al, Comparison measurements of low-pressure    between a laser refractometer and ultrasonic manometer, Rev. Sci.    Intrum. 87, 053113 (2016)-   [2] J Hendricks et al, The Emerging Field of Quantum Based    Measurements for Pressure, Vacuum and Beyond, J. Phys. Conf. Ser.    1065 162017 (2018)-   [3] Karl Jousten et al, Perspectives for a new realization of the    pascal by optical methods, Metrologia 54 S146 (2017)    https://doi.org/10.1088/1681-7575/aa8a4d-   [4] Jiang Li et al, Characterization of a high coherence, Brillouin    microcavity laser on silicon, Optics Express Vol. 20, p 20170 (2012)-   [5] Xingwang Zhang et al, Ultralow sensing limit in optofluidic    micro-bottle resonator biosensor by self-referenced    differential-mode detection scheme, Appl. Phys. Lett. 104, 033703    (2014); doi: 10.1063/1.4861596-   [6] William Loh et al, Ultra-Narrow Linewidth Brillouin Lasers with    Nanokelvin Thermometry, Optica 6 (2), 152-159 (2019)-   [7] Sarat Gundavarapu et al, Sub-hertz fundamental linewidth    photonic integrated Brillouin laser, Nature Photonics 13, pages    60-67 (2019)-   [8] Silander, T Hausmaninger, C Forssén, M Zelan, O Axner, Gas    equilibration gas modulation refractometry (GEq-GAMOR) for    assessment of pressure with sub-ppm precision, arXiv preprint    arXiv:1903.08424-   [9] Silander et al, Optical measurement of the gas number density in    a Fabry-Perot cavity, Meas. Sci. Technol. 24 (2013) 105207 (5 pp)-   [10] Julia Scherschligt et al, Quantum-based vacuum metrology at the    National Institute of Standards and Technology, Journal of Vacuum    Science & Technology A 36, 040801 (2018)-   [11] Patrick F. Egan, Cell-based refractometer for pascal    realization, Opt. Lett., 42, p 2944, (2017)-   [12] Patrick F. Egan, Jack A. Stone, Julia K. Scherschligt, and    Allan H. Harvey, Measured relationship between thermodynamic    pressure and refractivity for six candidate gases in laser    barometry, Journal of Vacuum Science & Technology A 37, 031603    (2019); https://doi.org/10.1116/1.5092185-   [13] C Gaiser and B Fellmuth, Polarizability of Helium, Neon, and    Argon: New Perspectives for Gas Metrology, Phys. Rev. Lett. 120,    123203 (2018)-   [14] Matthew T Hummon et al, Photonic chip for laser stabilization    to an atomic vapor with 10-11 instability, Optica 5 040443-07 (2018)-   [15] Patrick Egan and Jack Stone, Absolute refractometry of dry gas    to ±3 parts in 109, Applied Optics/Vol. 50 p 3076 (2011)-   [16] Laurent Vivian, Vertical multiple-slot waveguide ring    resonators in silicon nitride, Optics Express 16, p 17237 (2008)

Example 13

In some embodiments, a measurement includes setting a sequence ofpressures with the pressure controller and monitoring the photonicsensor. Multiple experimental variables are continuously logged into atext file. The main variable of interest is the inter-cavity beatfrequency. Pressure can be calculated from a simple proportionalitybetween pressure and frequency and the offset is adjusted.

The differential refractivity as a function of pressure leads to adifferential fractional frequency shift as a function of pressure:

$\frac{{df}/v_{0}}{dP} \approx {{2.7} \times 10^{- 9}/{{Pa}.}}$

Using this equation, we can convert from beat-note frequency to relativepressure. We can then use an arbitrary offset to match the pressuresmeasured by the pressure controller. An error is calculated by assumingthe pressure controller is ‘truth’ data.

After processing, raw frequency data is turned into pressure data andcan be compared to pressure controller measurements.

Example 14

With reference to FIG. 14 , lines in free-space in the cavity representthe paths that light would take for the measurement and referencecavities respectively, for example. The triangles represent a fiberconnector, and in the section between them the light travels infree-space. An element which is not shown, but can be included is a lensor a plurality of lenses between the two fiber connectors to couple thelight from one connector to the other with any efficiency. For example,a lens can be used as a collimator at each connector. The beam displacerdisplaces the light depending on its polarization and the lambda/2represents a half-wave plate, which rotates the polarization of anincoming beam. In some embodiments include separate counter-propagatingbeams, similar as in an isolator or circulator design.

Some pressure sensors disclosed herein include two cavities out of oneby using the clockwise and counter-clockwise modes of a single ringcavity. Some pressure sensors disclosed herein include some sectionwhere the two counter-propagating beams go through different paths sothat we can sense the different environment. Some pressure sensorsdisclosed herein include a ring cavity that is comprised of a length ofoptical fiber, a four-port fiber optic coupler (this plays the role ofan input and output mirror at the same time) and a free-space sectionwhere the beams are separated. Some pressure sensors disclosed hereinseparate clockwise and counter-clockwise beams by polarization usingbeam displacers.

Referring to FIG. 13 as an example, the distance between the cavity endmirrors (e.g., the top left round mirror and the back right slab mirror(the two mirrors on tangled facets)) determine the FSR. Correspondinglyfor the mirrors in the lower cavity.

The mode waist radius (which is radius of Gaussian intensity crosssection where the wavefront is flat) characterizes the beam crosssection at all other points inside the cavity. This is determined by thelength of the cavity and the radius of curvatures of the end mirrors).

Example 15: Exemplary Cavity Description

FIGS. 18A-18B and the description thereof is based on optical cavitiesin Notcutt, et al. (U.S. Pat. No. 10,141,712). FIGS. 18A and 18B are aperspective view and a cross-sectional view, respectively, of an opticalcavity 200, and are best viewed together in the following description.Optical cavity 200 is an exemplary cavity, such as a measurement cavityand/or a reference cavity, according to certain embodiments disclosedherein. Optical cavity 200 includes a first mirror 210, a second mirror220, and a resonator body 230 therebetween. Resonator body 230 has anend surface 232. First and second mirrors 210 and 220 have respectivereflective surfaces 212 and 222 separated by a cavity length 200L,hereinafter also referred to as L, along a cavity axis 202. Each ofreflective surfaces 212 and 222 may be either planar or non-planar. Thecross-sectional view of FIG. 18B is in a plane that includes cavity axis202. Optical cavity 100 may be rotationally symmetric about cavity axis202. Cavity length 200L is ten centimeters, for example. Surface 212 ofmirror 210 adjoins end surface 232 of resonator body 230. Surfaces 212and 232 may be directly bonded, via optical contact bonding and/orchemically activated direct bonding for example, such that no unwantedintermediate material is introduced between surfaces 212 and 232, orthat the extend of any unwanted intermediate material between surfaces212 and 232 is minimized.

Resonator body 230 may be formed of a material, such as a glass, havinga low coefficient of thermal expansion. Examples include, but are notlimited to, ULE® glasses by Corning, Inc., such as Corning 7972 glass,Corning 7973 glass, a high-temperature ULE® glass, Asahi A Z glass,sapphire, NEXCERA, AIIVar, Invar, and any combination thereof. Resonatorbody 230 may have a thermal coefficient of expansion of less than fiftyparts-per-billion-per-degree-Celsius (ppb/° C.) at temperatures between5° C. and 55° C.

Optical cavity 200 encloses a medium 250 that has a refractive index n₁.The internal volume of cavity 200 comprises medium 250. Medium 250 is,for example, vacuum or one or more gases. Optical cavity 200 has aresonance frequency v_(q)=qc/2 L+f₀, herein after Equation 1, where c isthe speed of light in vacuum and f₀ is an offset frequency. Integer qdenotes a first mode number. Quantity

$\frac{c}{2L}$

is the free-spectral range of cavity 100, FSR₁₀₀.

STATEMENTS REGARDING INCORPORATION BY REFERENCE AND VARIATIONS

All references throughout this application, for example patent documentsincluding issued or granted patents or equivalents; patent applicationpublications; and non-patent literature documents or other sourcematerial; are hereby incorporated by reference herein in theirentireties, as though individually incorporated by reference, to theextent each reference is at least partially not inconsistent with thedisclosure in this application (for example, a reference that ispartially inconsistent is incorporated by reference except for thepartially inconsistent portion of the reference).

The terms and expressions which have been employed herein are used asterms of description and not of limitation, and there is no intention inthe use of such terms and expressions of excluding any equivalents ofthe features shown and described or portions thereof, but it isrecognized that various modifications are possible within the scope ofthe invention claimed. Thus, it should be understood that although thepresent invention has been specifically disclosed by preferredembodiments, exemplary embodiments and optional features, modificationand variation of the concepts herein disclosed may be resorted to bythose skilled in the art, and that such modifications and variations areconsidered to be within the scope of this invention as defined by theappended claims. The specific embodiments provided herein are examplesof useful embodiments of the present invention and it will be apparentto one skilled in the art that the present invention may be carried outusing a large number of variations of the devices, device components,methods steps set forth in the present description. As will be obviousto one of skill in the art, methods and devices useful for the presentmethods can include a large number of optional composition andprocessing elements and steps.

As used herein and in the appended claims, the singular forms “a”, “an”,and “the” include plural reference unless the context clearly dictatesotherwise. Thus, for example, reference to “a cell” includes a pluralityof such cells and equivalents thereof known to those skilled in the art.As well, the terms “a” (or “an”), “one or more” and “at least one” canbe used interchangeably herein. It is also to be noted that the terms“comprising”, “including”, and “having” can be used interchangeably. Theexpression “of any of claims XX-YY” (wherein XX and YY refer to claimnumbers) is intended to provide a multiple dependent claim in thealternative form, and in some embodiments is interchangeable with theexpression “as in any one of claims XX-YY.”

When a group of substituents is disclosed herein, it is understood thatall individual members of that group and all subgroups, are disclosedseparately. When a Markush group or other grouping is used herein, allindividual members of the group and all combinations and subcombinationspossible of the group are intended to be individually included in thedisclosure.

Every sensor, device, system, mechanism, combination of components, ormethod described or exemplified herein can be used to practice theinvention, unless otherwise stated.

Whenever a range is given in the specification, for example, atemperature range, a time range, or a composition or concentrationrange, all intermediate ranges and subranges, as well as all individualvalues included in the ranges given are intended to be included in thedisclosure. It will be understood that any subranges or individualvalues in a range or subrange that are included in the descriptionherein can be excluded from the claims herein.

All patents and publications mentioned in the specification areindicative of the levels of skill of those skilled in the art to whichthe invention pertains. References cited herein are incorporated byreference herein in their entirety to indicate the state of the art asof their publication or filing date and it is intended that thisinformation can be employed herein, if needed, to exclude specificembodiments that are in the prior art. For example, when composition ofmatter are claimed, it should be understood that compounds known andavailable in the art prior to Applicant's invention, including compoundsfor which an enabling disclosure is provided in the references citedherein, are not intended to be included in the composition of matterclaims herein.

As used herein, “comprising” is synonymous with “including,”“containing,” or “characterized by,” and is inclusive or open-ended anddoes not exclude additional, unrecited elements or method steps. As usedherein, “consisting of” excludes any element, step, or ingredient notspecified in the claim element. As used herein, “consisting essentiallyof” does not exclude materials or steps that do not materially affectthe basic and novel characteristics of the claim. In each instanceherein any of the terms “comprising”, “consisting essentially of” and“consisting of” may be replaced with either of the other two terms. Theinvention illustratively described herein suitably may be practiced inthe absence of any element or elements, limitation or limitations whichis not specifically disclosed herein.

One of ordinary skill in the art will appreciate that system componentssuch as certain optical or electrical devices or components can beemployed in the practice of the invention without resort to undueexperimentation. All art-known functional equivalents of any suchmaterials, devices, components, systems, and methods are intended to beincluded in this invention. The terms and expressions which have beenemployed are used as terms of description and not of limitation, andthere is no intention that in the use of such terms and expressions ofexcluding any equivalents of the features shown and described orportions thereof, but it is recognized that various modifications arepossible within the scope of the invention claimed. Thus, it should beunderstood that although the present invention has been specificallydisclosed by preferred embodiments and optional features, modificationand variation of the concepts herein disclosed may be resorted to bythose skilled in the art, and that such modifications and variations areconsidered to be within the scope of this invention as defined by theappended claims.

We claim:
 1. A pressure sensor for determining pressure in anenvironment, comprising: a first source for emitting a coherentreference light characterized by a reference light frequency; a firstoptical circulator in optical communication with the first source via anoptical fiber; a second source for emitting a measurement coherent lightcharacterized by a measurement light frequency; a second opticalcirculator in optical communication with the second source via anoptical fiber; a fiber optic coupler in optical communication with thefirst optical circulator via an optical fiber and with the secondoptical circulator via an optical fiber; a reference cavity in opticalcommunication with the fiber optic coupler via an optical fiber andconfigured to receive at least a portion of the coherent reference lightfrom the fiber optic coupler; wherein the reference cavity ischaracterized by the reference resonance frequency; and wherein apressure in a reference space of the reference cavity is less than orequal to 0.1 mTorr; a measurement cavity in optical communication withthe fiber optic coupler via an optical fiber and configured to receiveat least a portion of the measurement light from the fiber opticcoupler; wherein the measurement cavity is characterized by themeasurement resonance frequency; a measurement lock-in mechanism inoptical communication with the first fiber optical circulator via anoptical fiber and configured to send an electrical signal at least tothe second source based on at least the measurement resonance frequency;and a reference lock-in mechanism in optical communication with thesecond fiber optical circulator via an optical fiber and configured tosend an electrical signal at least to the first source based on at leastthe reference resonance frequency; wherein the pressure of theenvironment is determined based on the reference resonant frequency andthe measurement resonance frequency.
 2. The pressure sensor of claim 1,wherein the measurement lock-in mechanism is in electrical communicationwith a processing mechanism configured to determine the pressure of theenvironment based on the reference resonant frequency and themeasurement resonance frequency.
 3. The pressure sensor of claim 1,wherein the measurement lock-in mechanism comprises a first opticaldetector and a first error signal modulator, wherein the first opticaldetector is in electrical communication with the first error signalmodulator and the first error signal modulator is in electricalcommunication with the second source.
 4. The pressure sensor of claim 1,wherein the reference lock-in mechanism comprises a second opticaldetector and a second error signal modulator, wherein the second opticaldetector is in electrical communication with the second error signalmodulator and the second error signal modulator is in electricalcommunication with the first source.
 5. The pressure sensor of claim 3,wherein the reference coherent light is characterized by a first atleast one phase modulation frequency and wherein the first error signalmodulator generates the first at least one phase modulation frequency ofthe measurement light.
 6. The pressure sensor of claim 3, wherein themeasurement light is characterized by a second at least one phasemodulation frequency and wherein the second error signal modulatorgenerates the second at least one phase modulation frequency of thereference coherent light.
 7. The pressure sensor of claim 1, wherein thereference cavity and the measurement cavity are formed using a resonatorbody and a plurality of mirrors, and wherein the mirrors arecharacterized by a radius of curvature selected from the range of 1 cmto 1 m.
 8. The pressure sensor of claim 1 comprising at least one fiberresonator, the fiber resonator comprising the reference cavity and themeasurement cavity and the fiber resonator being characterized by thereference resonant frequency and the measurement resonance frequency,respectively.
 9. The pressure sensor of claim 8, wherein the referencecavity or the reference resonance frequency corresponds to a referencemode of the fiber resonator and the measurement cavity or themeasurement resonance frequency corresponds to a measurement mode of thefiber resonator being.
 10. The pressure sensor of claim 9, wherein thereference mode of the fiber resonator and the measurement mode of thefiber resonator are characterized by a different light polarization modewith respect to each other.
 11. The pressure sensor of claim 9, whereinthe reference mode of the fiber resonator and the measurement mode ofthe fiber resonator are characterized by a different light propagationmode with respect to each other.
 12. The pressure sensor of claim 1,wherein at least a fraction of light in the measurement cavitypropagates in a direction that is opposite of a direction propagated byat least a fraction of light in the reference cavity.
 13. The pressuresensor of claim 9, wherein the fiber resonator comprises apolarization-maintaining optical fiber having at least the referencemode and the measurement mode; wherein the reference mode corresponds toa first light polarization mode of the polarization-maintaining opticalfiber and the measurement mode corresponds to a second lightpolarization mode of the polarization-maintaining optical fiber.
 14. Thepressure sensor of claim 9, wherein the fiber resonator comprises amulti-mode optical fiber having at least the reference mode and themeasurement mode; wherein the reference mode corresponds to a firstlight propagation mode of the multi-mode optical fiber and themeasurement mode corresponds to a second light propagation mode of themulti-mode optical fiber.
 15. The pressure sensor of claim 8, wherein aportion of the fiber resonator corresponding to a portion of themeasurement cavity is open to the environment, such that lightassociated with the measurement cavity in the fiber resonator is exposedto the environment.
 16. The pressure sensor of claim 8, wherein aportion of the fiber resonator corresponding to a portion of thereference cavity is open to the reference space, such that lightassociated with the reference cavity in the fiber resonator is exposedto the reference space; wherein the reference space is characterized bya pressure less than or equal to 0.1 mTorr.
 17. The pressure sensor ofclaim 8, comprising stimulated Brillouin scattering in the fiberresonator.
 18. The pressure sensor of claim 1, wherein the referencecavity and the measurement cavity are in optical communication with atleast one beam displacer configured to displace light based on itspolarization.
 19. The pressure sensor of claim 1, wherein the referencecavity and the measurement cavity are in optical communication with atleast one half-wave plate.
 20. The pressure sensor of claim 1, whereineach of the at least one beam displacer combines light associated withthe reference cavity with light associated with the measurement cavity.21. The pressure sensor of claim 1, wherein the first source is a pumplaser.
 22. The pressure sensor of claim 1, wherein each of the referencecavity and the measurement cavity is independently characterized by athermal time constant of less than 1000 seconds.
 23. The pressure sensorof claim 1 wherein the pressure sensor is characterized by anintermediate total error of less than or equal to 100±20 ppm.
 24. Thepressure sensor of claim 1, wherein the pressure sensor is characterizedby a free spectral range of less than or equal to 200 MHz.
 25. Thepressure sensor of claim 1, wherein the pressure sensor is characterizedby a finesse selected from the range of 100 to 200,000.
 26. The pressuresensor of claim 1, wherein each of the measurement cavity and thereference cavity is characterized by a mode waist radius selected fromthe range of 50 μm to 500 μm.